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测量多边形面积

测量多边形面积
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2019-04-02 01:19
多边形向量解析几何几何作图
①本范例演示如何使用 GeoGebra 测量任意多边形的面积；②涉及的核心数学概念包括向量、几何变换、多边形构造与坐标几何；③作图要点：使用 Segment, Vector, Point, Rotate, Polygon, Max, Min, Translate 等命令构建多边形并计算面积；④适合高中数学教学，用于理解多边形面积计算方法及向量应用。

GeoGebra 命令及参数

  1. Segment(X0, X0 + (0, mark)) → h
  2. Segment(X0 + (1, 0), X0 + (1, mark)) → i
  3. Vector(X0 + (0, mark / 2), X0 + (1, mark / 2)) → u
  4. Vector(X0 + (1, mark / 2), X0 + (0, mark / 2)) → v
  5. Segment(Y0 - (mark, 0), Y0) → j
  6. Segment(Y0 - (mark, 1), Y0 - (0, 1)) → k
  7. Vector(Y0 - (mark / 2, 1), Y0 - (mark / 2, 0)) → w
  8. Vector(Y0 - (mark / 2, 0), Y0 - (mark / 2, 1)) → z
  9. Point(yAxis) → A
  10. Point(xAxis) → B
  11. Point(xAxis) → C
  12. Rotate(E, (90° * t1), F) → E'
  13. Rotate(F, (90° * t1), F) → F'
  14. Rotate(L, (90° * t1), F) → L'
  15. Polygon(E', F', L') → poly1, l', e', f'
  16. Rotate(G, ((-(90°)) * t2), F) → G'
  17. Rotate(M, ((-(90°)) * t2), F) → M'
  18. Rotate(F, ((-(90°)) * t2), F) → F'_1
  19. Polygon(G', M', F'_1) → poly2, f'_1, g', m'
  20. Rotate(D, ((-(180°)) * t3), J) → D'
  21. Rotate(E, ((-(180°)) * t3), J) → E'_1
  22. Rotate(J, ((-(180°)) * t3), J) → J'
  23. Polygon(D', E'_1, J') → poly3, j', d', e'_1
  24. Rotate(J, (180° * t4), J) → J'_1
  25. Rotate(K, (180° * t4), J) → K'
  26. Rotate(C, (180° * t4), J) → C'
  27. Polygon(J'_1, K', C') → poly4, c', j'_1, k'
  28. Max(t5 - 1, 0) → s2
  29. Min(t5, 1) → s1
  30. Min(t6, 1) → w1
  31. Max(t6 - 1, 0) → w2
  32. Translate(Translate[G, Vector[(s1 * Vector[M, H])]], Vector[(s2 * Vector[M, B])]) → G''
  33. Translate(Translate[M, Vector[(s1 * Vector[M, H])]], Vector[(s2 * Vector[M, B])]) → M''
  34. Translate(Translate[H, Vector[(s1 * Vector[H, M])]], Vector[(s2 * Vector[M, B])]) → H''
  35. Polygon(G'', H'', M'') → poly5, m'', g'', h''
  36. Translate(Translate[B, Vector[(w1 * Vector[N, A])]], Vector[(w2 * Vector[B, M])]) → B'
  37. Translate(Translate[N, Vector[(w1 * Vector[N, A])]], Vector[(w2 * Vector[B, M])]) → N'
  38. Translate(Translate[A, Vector[(w1 * Vector[A, N])]], Vector[(w2 * Vector[B, M])]) → A'
  39. Polygon(A', B', N') → poly6, n', a', b'
  40. Polygon(E', F', L') → poly1', l'_1, e'_2, f'_2
  41. Polygon(G', M', F'_1) → poly2', f'_3, g'_1, m'_1
  42. Polygon(D', E'_1, J') → poly3', j'_2, d'_1, e'_3
  43. Polygon(J'_1, K', C') → poly4', c'_1, j'_3, k'_1
  44. Polygon(G'', H'', M'') → poly5', m''_1, g''_1, h''_1
  45. Polygon(A', B', N') → poly6', n'_1, a'_1, b'_1
  46. Polygon(H, I, N, B, C, K, J, L) → poly7, h_1, i_1, n, b, c, k_1, j_1, l
  47. Polygon(A, B, C, D, E, F, G, H, I) → poly8, a, b_1, c_1, d, e, f, g, h_2, i_2
  48. Polygon(E, F, L) → poly9, l_1, e_1, f_1
  49. Polygon(F, G, M) → poly10, m, f_2, g_1
  50. Polygon(G, H, M) → poly11, m_1, g_2, h_3
  51. Polygon(A, B, N) → poly12, n_1, a_1, b_2
  52. Polygon(C, K, J) → poly13, j_2, c_2, k_2
  53. Polygon(D, E, J) → poly14, j_3, d_1, e_2